arens_aud16_inppt17.pptx Auditing and assurance services

Auditing and assurance services arens book 16 edition chapter 17 ppt

1. Audit sampling for tests of details of balances Chapter 17 Copyright © 2017 Pearson Education, Ltd. 17-1

2. Chap ter 17 Learning Objectives 17-1 Differentiate audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions. 17-2 Apply nonstatistical sampling to tests of details of balances. 17-3 Apply monetary unit sampling. 17-4 Describe variables sampling. 17-5 Use difference estimation in tests of details of balances. Copyright © 2017 Pearson Education, Ltd. 17- 2

3. Copyright © 2017 Pearson Education, Ltd. 17- 3 OBJECTIVE 17-1 Differentiate audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions .

4. Comparisons of audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions The main differences among tests of controls, substantive tests of transactions, and tests of details of balances are in what the auditor wants to measure. Copyright © 2017 Pearson Education, Ltd. 17- 4

5. Copyright © 2017 Pearson Education, Ltd. 17- 5 OBJECTIVE 17-2 Apply nonstatistical sampling to tests of details of balances .

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7. Nonstatistical sampling (cont.) State the Objectives of the Audit Test : Auditors sample for tests of details of balances to determine whether the account balance is fairly stated. Decide Whether Audit Sampling Applies : Audit sampling applies whenever the auditor plans to reach conclusions about a population based on a sample. Define a Misstatement : Because audit sampling for tests of details of balances measures monetary misstatements, a misstatement exists whenever a sample item is misstated. Define the Population : The items making up the recorded dollar population . The auditor may separate the population into subpopulations before applying audit sampling. Table 17-1 is an illustrative sample of an accounts receivable population. Copyright © 2017 Pearson Education, Ltd. 17- 7

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9. Nonstatistical sampling (cont.) Define the Sampling Unit : For nonstatistical audit sampling in tests of details of balances, the sampling unit is almost always the items making up the account balance. Specify the Tolerable Misstatement : The application of performance materiality to a particular sampling procedure. Specify Acceptable Risk of Incorrect Acceptance : The acceptable risk of incorrect acceptance (ARIA) is the risk that the sample supports the conclusion that the recorded account balance is not materially misstated when it is materially misstated. Figure 17-1 shows the effect of ARO and ARIA on substantive testing. The relationships affecting ARIA are summarized in Table 17-2 . Copyright © 2017 Pearson Education, Ltd. 17- 9

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12. Nonstatistical sampling (cont.) Estimate Misstatements in the Population : Auditor typically makes this estimate based on prior experience with the client and by assessing inherent risk, considering the results of tests of controls, substantive tests of transactions, and analytical procedures already performed. Determine the Initial Sample Size : When using nonstatistical sampling, auditors determine the initial sample size by considering the factors that are summarized in Table 17-3 . Figure 17-2 presents a simple formula for computing sample size based on the AICPA Audit Sampling Audit Guide. Select the Sample : Auditing standards permit the auditor to use any of the selection methods discussed in Chapter 15. Copyright © 2017 Pearson Education, Ltd. 17- 12

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15. Nonstatistical sampling (cont.) Perform the Audit Procedures : The auditor applies the appropriate audit procedures to each item in the sample to determine whether it contains a misstatement. Generalize from the Sample to the Population and Decide the Acceptability of the Population : The auditor should generalize the sample to the population by (1) projecting misstatements from the sample to the population and (2) considering sampling risk (ARIA). This starts with calculating a point estimate , which is usually done by assuming that the misstatement in the population is proportional to the misstatement in the sample. Analyze the Misstatement : The auditor must evaluate the nature and cause of each misstatement found in the tests of details of balances. Copyright © 2017 Pearson Education, Ltd. 17- 15

16. Nonstatistical sampling (cont.) Action When a Population Is Rejected : When the auditor concludes that the misstatement in a population may be larger than tolerable misstatement after considering sampling risk, the auditor has several courses of action. Take no action until tests of other audit areas are complete. Perform expanded audit tests in specific areas. Increase the sample size. Adjust the account balance. Request the client to correct the population. Refuse to give an unmodified opinion. Copyright © 2017 Pearson Education, Ltd. 17- 16

17. Copyright © 2017 Pearson Education, Ltd. 17- 17 OBJECTIVE 17-3 Apply monetary unit sampling .

18. Monetary Unit sampling Copyright © 2017 Pearson Education, Ltd. 17- 18 Monetary unit sampling is the most common statistical method of sampling for tests of details of balances because it has the statistical simplicity of attributes sampling yet provides a statistical result expressed in dollars. Difference Between Monetary Unit Sampling and Nonstatistical Sampling : The definition of the sampling unit is an individual dollar. The population size is the recorded dollar population. Sample size is determined using a formula. Sample selection is done using PPS (probability proportional to size sample selection). A typical accounts receivable population is shown in Table 17-4 . The auditor generalizes from the sample to the population using MUS.

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20. Monetary Unit sampling (cont.) Decide the Acceptability of the Population Using MUS: The auditor compares the calculated misstatement bound to tolerable misstatement. If the bound exceeds the tolerable misstatement, the population is not considered acceptable. Determining Sample Sizes Using MUS: The following factors are used in computing sample size: Acceptable Risk of Incorrect Acceptance (ARIA)— This is dependent on the audit risk factors. Recorded Population Value— The dollar value of the population taken from the client’s records. Tolerable Misstatement— Generally the same as performance materiality. Copyright © 2017 Pearson Education, Ltd. 17- 20

21. Monetary Unit sampling (cont.) Determining Sample Size Using MUS: The following factors are used in computing sample size (cont.): Tolerable Misstatement as a Percentage of Population Value Estimated Population Misstatement— This is usually based on the sample results for the prior year. Ratio of Estimated Population Misstatement to Tolerable Misstatement Confidence Factor— The auditor uses Table 17-5 to determine the appropriate confidence factor based on the auditor’s judgment of ARIA and the ratio of expected misstatement to tolerable misstatement. Copyright © 2017 Pearson Education, Ltd. 17- 21

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23. Monetary Unit sampling (cont.) Determining Sample Sizes Using MUS: The following factors are used in computing sample size (cont.): Sample Size— Example calculated as follows: Sampling Interval— The population recorded amount divided by the sample size. Table 17-6 summarizes the steps to calculate sample size in MUS. Copyright © 2017 Pearson Education, Ltd. 17- 23

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25. Monetary Unit sampling (cont.) Generalizing from the Sample to the Population When No Misstatements Are Found Using MUS: If the entire sample is audited and no misstatements are found in the sample, the auditor may conclude that the recorded amount of the population is not overstated by more than the tolerable misstatement at the specified risk of incorrect acceptance. The upper limit when no misstatements are found is the confidence factor for no misstatements multiplied by the length of the sampling interval. The upper limit is also referred to as basic precision . Table 17-7 shows the confidence factors for MUS sample evaluation. Copyright © 2017 Pearson Education, Ltd. 17- 25

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27. Monetary Unit sampling (cont.) Generalizing from the Sample to the Population When Misstatements A re Found Using MUS: Assume that the auditor tested the sample and found the three overstatements included in Table 17-8. Calculating the upper misstatement bound involves three steps: Calculate the percentage misstatement for each misstatement. Project the sample misstatements by multiplying the percentage misstatement by the length of the sampling interval. Add an allowance for sampling risk based on the confidence factors for the actual number of misstatements and acceptable risk of incorrect acceptance. Copyright © 2017 Pearson Education, Ltd. 17- 27

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29. Monetary Unit sampling (cont.) Generalizing from the Sample to the Population When Misstatements A re Found Using MUS (cont.): Calculate Percentage Misstatement Assumption (Tainting): When misstatements are found, the auditor calculates a projected misstatement and an allowance for sampling risk. This is illustrated in Table 17-8 . Project Sample Misstatements: The projected misstatement is the percentage misstatement times the sampling interval. The calculation of projected misstatement for the three actual sample misstatements is shown in Table 17-9 . Copyright © 2017 Pearson Education, Ltd. 17- 29

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31. Monetary Unit sampling (cont.) Generalizing from the Sample to the Population When Misstatements A re Found Using MUS (cont.): Calculate the Allowance for Sampling Risk: The projected misstatement is increased by the allowance for sampling risk, which is calculated as basic precision plus an incremental allowance for sampling risk for each misstatement found in sampling units that are smaller than the sampling interval. Table 17-10 provides an example of the incremental changes in the confidence factor for five misstatements and a 5% ARIA. Relationship of the Audit Risk Model to Sample Size for MUS: Auditors must understand the relationships of the three independent factors in the audit risk model. Copyright © 2017 Pearson Education, Ltd. 17- 31

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33. Monetary Unit sampling (cont.) Audit Uses of Monetary Unit Sampling: MUS appeals to auditors for at least four reasons: MUS automatically increases the likelihood of selecting high dollar items from the population. MUS often reduces the cost of doing the audit testing because several sample items are tested at once MUS is easy to apply. Samples can be evaluated by the application of simple tables. MUS provides a statistical conclusion rather than a nonstatistical one, providing better and more defensible decisions. Copyright © 2017 Pearson Education, Ltd. 17- 33

34. Monetary Unit sampling (cont.) Audit Uses of Monetary Unit Sampling: There are two main disadvantages of MUS: The total misstatement bounds resulting when misstatements are found may be too high to be useful to the auditor. To overcome this problem, larger samples may be required. It may be cumbersome to select PPS samples from large populations without computer assistance. For all of these reasons, auditors commonly use MUS when zero or few misstatements are expected, a dollar result is desired, and the population data are accessible in electronic format. Copyright © 2017 Pearson Education, Ltd. 17- 34

35. Copyright © 2017 Pearson Education, Ltd. 17- 35 OBJECTIVE 17-4 Describe variables sampling .

36. Variables sampling Copyright © 2017 Pearson Education, Ltd. 17- 36 Like MUS, variables sampling is a statistical sampling method. Differences Between Variable and Nonstatistical Sampling: These methods share many similarities. Sampling Distribution: It is useful to understand sampling distributions and how they affect auditor’s statistical conclusions. The auditor does not know the mean value of misstatements in the population, the distribution of the misstatement amounts, or the audited values. These population characteristics must be estimated from samples.

37. Variables sampling (cont.) Sampling Distribution ( cont ): The auditor calculates the mean value of items in the sample as follows: Copyright © 2017 Pearson Education, Ltd. 17- 37

38. Variables sampling (cont.) Sampling Distribution ( cont ): After this calculation of each sample, the auditor plots them into a frequency distribution. As long as the sample size is sufficient, the frequency distribution will appear much like that shown in Figure 17-3 . The distribution of the sample means such as this is normal and has all the characteristics of the normal curve: The curve is symmetrical The sample means fall within known portions of the sampling distribution around the average mean of those means. Furthermore, the mean of the sample means is equal to the population mean. Copyright © 2017 Pearson Education, Ltd. 17- 38

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40. Variables sampling (cont.) Sampling Distribution ( cont ): With this information, the auditors can make the tabulation of the sampling distribution as shown in Table 17-11 . To summarize, three things shape the results of the experiment of taking a large number of samples from a known population: The mean value of all the samples is equal to the population mean. The shape of the frequency distribution of the sample means is that of a normal distribution, as long as the sample size is sufficiently large, regardless of the distribution of the population , as illustrated in Figure 17-4 . The percentage of sample means between any two values of the sampling distribution is measurable. Copyright © 2017 Pearson Education, Ltd. 17- 40

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43. Variables sampling (cont.) Statistical Inference: When samples are taken from a population in an actual audit, the auditor does not know the population’s characteristics, and ordinarily, only one sample is taken from the population. But the knowledge of sampling distributions enables auditors to draw statistical conclusions, or statistical inferences , about the population. An example of this process is shown on pages 585 and 586. Auditors can state the conclusions drawn from a confidence interval using statistical inferences in different ways, taking care to avoid incorrect conclusions because the true population value is always unknown. Copyright © 2017 Pearson Education, Ltd. 17- 43

44. Variables sampling (cont.) Variables Methods: Auditors use the preceding statistical inference process for all of the variable sampling methods. The three variables methods include: Difference Estimation— Auditors use difference estimation to measure the estimated total misstatement amount in a population when both the recorded value and an audited value exist for each item in the sample. Ratio Estimation— Similar to difference estimation except the auditor calculates the ratio between the misstatements and their recorded value and projects this to the population to estimate the total population misstatement. Mean-per-Unit Estimation— The auditor focuses on the audited value rather than the misstatement amount of each item in the sample. Copyright © 2017 Pearson Education, Ltd. 17- 44

45. Variables sampling (cont.) Stratified Statistical Methods: As with other stratified methods, the population is divided into two or more subpopulations. Each is independently tested and evaluated, and the results combined. This can be used with any of the variables methods, but is most commonly used with mean- p er-unit estimation. Sampling Risks: In addition to acceptable risk of incorrect acceptance (ARIA), auditors use acceptable risk of incorrect rejection (ARIR) for variables sampling. ARIA—The risk that the auditor accepts a population that is materially misstated. ARIR—The risk that the auditor has concluded that a population is materially misstated when it is not. These are illustrated in Tables 17-12 and 17-13 . Copyright © 2017 Pearson Education, Ltd. 17- 45

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48. Copyright © 2017 Pearson Education, Ltd. 17- 48 OBJECTIVE 17-5 Use difference estimation in tests of details of balances .

49. Illustration using difference estimation Copyright © 2017 Pearson Education, Ltd. 17- 49 Plan the Sample and Calculate the Sample Size Using Difference Estimation: Accounts Receivable consists of 4,000 accounts with a recorded value of $600,000. Tolerable misstatement is $21,000. Specify Acceptable Risk— The auditor specifies two risks: Acceptable risk of incorrect acceptance (ARIA)—10% Acceptable risk of incorrect rejection (ARIR)—25% Estimate Misstatements in the Population: Estimate an expected point estimate. Make an advance population standard deviation estimate—variability of the population.

50. Illustration using difference estimation (cont.) Plan the Sample and Calculate the Sample Size Using Difference Estimation ( cont ): Calculate the Initial Sample Size: The calculation of the sample size is shown on page 589. Sample size is 100. Evaluate the Results: Generalize from the Sample to the Population: The calculations are illustrated in Table 17-14 on pages 590–591. Copyright © 2017 Pearson Education, Ltd. 17- 50